Technically speaking then. Any stock that pays out Dividends is doing the same operation as BT.
Just to note: I treat BTC as stock. Because stock's value changes and is used as monetary compensation; aka Stock Options (during hiring or during company mergers).
In this case BT's business is to buy and sell BTC, hopefully at a profit at the end of the day (literally). Just as a company's business is to sell its services and at the end of the day (yearly/quarterly) make a profit.
From those profits a percentage is designated to be paid out to investors; Dividends.
I suppose, technically, you could look at it that way. Similarly, MMM, Bitcoin Savings and Trust and countless other ponzis paid out money to "investors", until they didn't. Also, as juanbond stated above, a traditional public company's dividends are no where near what BT has been paying.
Another problem with I have with your comparison is that BT (and most every other ponzi) is more like a "black box". You have to trust them completely, there is no way to verify any of the information they are providing you. Unlike public companies that trade on traditional exchanges, there are no audits, no financial records, no proof or evidence of anything they tell you. Trusting them is, for me, very hard to do because they are not financing their operations in a logical manner. As described previously, if legitimate, they are funding their business in the most expensive and labor intensive way possible.
They appear to be operating their business exactly like a ponzi, why should I trust them and think they are different?
As a side note, BT claims to be use arbitrage, which is hardly "buy and sell, hopefully at a profit". Generally arbitrage is "risk free", except for trade execution errors or exchange theft (applicable in the bitcoin world).